{"paper":{"title":"The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nikolas Kuhn, Oliver Leigh, Yuuji Tanaka","submitted_at":"2022-05-25T17:58:34Z","abstract_excerpt":"We prove a blow-up formula for the generating series of virtual $\\chi_y$-genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for topological $\\chi_y$-genera of G\\\"ottsche. Our formula is a refinement of one by Vafa-Witten relating to S-duality. We prove the formula simultaneously in the setting of Gieseker stable sheaves on polarised surfaces and also in the setting of framed sheaves on $\\mathbb{P}^2$. The proof is based on the blow-up algorithm of Nakajima-Yoshioka for framed sheaves on $\\mathbb{P}^2$, which has recently been extend to the set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.12953","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.12953/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}